1.1
List the math classes you have taken during high school. Write a few sentences describing your feelings toward math and why - either a good experience or a bad one. Think about what type of learner you are describe the best methods teachers use to help you understand the topics. Please describe your goals after this year - do you need this class to graduate and you are a senior, are you here for MCAS reasons, or what math class or classes do you plan on taking next year?
My freshman year I took Algebra 1 Honors and i enjoyed that class it was fun. My sophomore year I took Geometry Honors and I hated it I didn't understand one thing. Right now im currently in my junior year and im taking Algebra 2 CP and so far i like it. Well my opinion about math is that I always hated it because im slow at it and didn't understand it as fast as other students and needed more help. Last year when I took Geometry I was horrible at I had so much trouble I didn't understand much and I didn't really like to ask questions. Im a visual learner and I don't really like to ask questions during class. My goal this year is to do great and learn as much as I possibly can. Im taking this class because I need for me to graduate. Im not completely sure about what math class im taking next year. I haven't really thought about that yet.
1.2
Look at the following, which is an example that has been worked out step by step. Explain in full sentences each step that was taken in the problem and why that step was chosen. Be clear about the step you are looking at, for example "going from line 1 to line 2, ..." All these steps should be written in your online journal.
The first problem is worked out correctly and step by step. In step number 2 the whole problem was multiplied by 10 because it was the least common denominator with the number 2 and 5. Then in step 3 6x is subtracted by 1x to get the variables all on one side so its easier to isolate the variable. Then in step 4 -20 is added to 40 which isolates the variable. Then the last step is to divide -60 by -1 and we get the answer 60.
[Note: I like your goal for the year! In 1.2, what happens after you get an answer of 60? There were more steps after that one... -Mr. G]
1.3
After spending time in class and at home solving a variety of equations, identify the type of problem that is the easiest for you to solve. Also identify the type of problem that you struggle with the most. Why is this type of problem the most challenging? Where do you make your errors most often? What tricks or reminders should you write here (in a different color) as a reminder to prevent that error in the future?
The easiest type of problem for me is finding a common multiple. The type I struggle with more is the decimal one because just having a decimal in a problem confuses me. Its more challenging because of seeing the decimal points there because when adding, subtracting, multiplying, and dividing the decimals can move around. What messes me up more is the negative signs they always get to me and get me confused. If could just remember thata negative x a negative = a positive & a negative x a postive = a negative & a positive x a positive = a positive same with dividing.
1.4
List the following words and give a mathematical definition in your own words on your wikispace.
Linear Function
Relation
Domain
Range
Increasing
Decreasing
Slope
Intercept
Degree
If you need assistance defining any of the words above, this site may be helpful... Vocabulary Help
Linear function: a polynomial equation at the first degree
Relation: an abstraction belonging to or characteristic of two entities or parts together
Domain: the set of values of the independent variable for which a function is defined
Range: the set of values of the dependent variable for which a function is defined
Increasing: becoming greater or larger
Decreasing: becoming less or smaller
Slope: an elevated geological formation
Intercept: seize on its way
Degree: the degree of the term in the polynomial that has the highest degree
1.6
Below there is a document which 4 linear graphs shown and 6 linear equations given. In a paragraph, describe how you matched each equation to its matching graph and the order in which you matched them. What graphical features did you look at or which parts of that equation did you focus on?
Graph A is #8 f(x)= -1/3x-4 Graph B is #2 f(x)= 2x+4 Graph C is #6 f(x)= -1/2x-4 Graph D is #7 f(x)= 1/3x+4
To match the equation with the graph I looked at the graphs y-intercept and I did rise over run and then I would just check the equations to make sure they matched and if they were correct. Also I checked the direction that the graph is going if its positive or negative.
1.7
Below there is a document which 4 linear graphs shown and 12 linear equations given. In a paragraph, describe how you matched each equation to its matching graph and the order in which you matched them. Each graph matches one linear function in slope-intercept form and one linear function in standard form There should be two equations per graph. Did you match equivalent functions first or did you try to match each function to a graph first? What graphical features did you look at or which parts of that equation did you focus on?
Graph A is #4 f(x)= -2x+3 & c 4x+2y=6 Graph B is #1 f(x)= -2/3x+1 & b 2x+3y=3 Graph C is #5 f(x)= 3x+2 & a -3x+y=2 Graph D is #3 f(x)= 2x+3 & d -6x+3y=9
I graphed the y-intercept slope form first and after that I changed all the standard forms to y-intercept slope form and put the matching ones together.
1.8
Using the graph below:
Complete the following table
Write a paragraph describing the walking pattern shown. Use as much detail as possible so that some one would be able to recreate this graph from your description.
For the first minute Ann drove to school and she went up to a speed of 30 miles per hour. For 4 minutes Ann drove at a steady pace of 30 miles per hour then after those 4 minutes Ann stopped for 1 minute then started driving again going at a steady pace of 40 miles per hour for 3 minutes then her speed went down to a speed of 20 miles per hour for 5 minutes then a minute later she stopped driving.
1.8.jpg
Answer the following questions:
When is Anne driving the fastest? Explain how you found your answer.
What time is Anne stopped? Explain how you found your answer.
When is Anne's speed decreasing? Explain how you arrived at your answer.
What is Anne's speed at 7 minutes?
At what approximate time is Ann driving 35 mph?
From 5 to 9 minutes Ann is driving at 40 miles per hour i looked at where the line was at its highest.
Between 4.5 minutes and 5 Ann is stopped and at 12 minutes Ann is also stopped.
At 4 minutes and 8 minutes and 11.5 minutes I looked at where the line is going down.
40 miles per hour.
Between 6 to 8 minutes.
1.9
In your classroom binder, title a page "Introduction to Graphical Transformations".
Copy f(x) onto the page and create a table of values using x-values 0 through 4.
On the right side, sketch a graph and plot each of the five points from your table in a different color.
Connect the dots with your pencil to create a linear graph.
Back on the left side, copy down g(x) and create a table of values for x-values 1 - 5.
On the SAME GRAPH, plot each of the 4 points from your g(x) table with the same four colors you used before and in the same color order.
f(x)=1/2x
g(x)=1/2(x - 1) + 4
You can use the following document link to help you set up your table of values and graphs if necessary. 1.9 journal response.doc
After completing the table of values and graphs, in your online journal, describe anything you observe about the relationship of the matching coordinate points. Try to relate this thinking to the equation of g(x).
What I noticed about the relationship of these coordinate points is that they are parallel to each other and that they are both linear also that it goes up 4 units and across to the right 1 unit.
List the math classes you have taken during high school. Write a few sentences describing your feelings toward math and why - either a good experience or a bad one. Think about what type of learner you are describe the best methods teachers use to help you understand the topics. Please describe your goals after this year - do you need this class to graduate and you are a senior, are you here for MCAS reasons, or what math class or classes do you plan on taking next year?
My freshman year I took Algebra 1 Honors and i enjoyed that class it was fun. My sophomore year I took Geometry Honors and I hated it I didn't understand one thing. Right now im currently in my junior year and im taking Algebra 2 CP and so far i like it. Well my opinion about math is that I always hated it because im slow at it and didn't understand it as fast as other students and needed more help. Last year when I took Geometry I was horrible at I had so much trouble I didn't understand much and I didn't really like to ask questions. Im a visual learner and I don't really like to ask questions during class. My goal this year is to do great and learn as much as I possibly can. Im taking this class because I need for me to graduate. Im not completely sure about what math class im taking next year. I haven't really thought about that yet.
1.2
Look at the following, which is an example that has been worked out step by step. Explain in full sentences each step that was taken in the problem and why that step was chosen. Be clear about the step you are looking at, for example "going from line 1 to line 2, ..." All these steps should be written in your online journal.
The first problem is worked out correctly and step by step. In step number 2 the whole problem was multiplied by 10 because it was the least common denominator with the number 2 and 5. Then in step 3 6x is subtracted by 1x to get the variables all on one side so its easier to isolate the variable. Then in step 4 -20 is added to 40 which isolates the variable. Then the last step is to divide -60 by -1 and we get the answer 60.
[Note: I like your goal for the year! In 1.2, what happens after you get an answer of 60? There were more steps after that one... -Mr. G]
1.3
After spending time in class and at home solving a variety of equations, identify the type of problem that is the easiest for you to solve. Also identify the type of problem that you struggle with the most. Why is this type of problem the most challenging? Where do you make your errors most often? What tricks or reminders should you write here (in a different color) as a reminder to prevent that error in the future?
The easiest type of problem for me is finding a common multiple. The type I struggle with more is the decimal one because just having a decimal in a problem confuses me. Its more challenging because of seeing the decimal points there because when adding, subtracting, multiplying, and dividing the decimals can move around. What messes me up more is the negative signs they always get to me and get me confused. If could just remember that a negative x a negative = a positive & a negative x a postive = a negative & a positive x a positive = a positive same with dividing.
1.4
List the following words and give a mathematical definition in your own words on your wikispace.
If you need assistance defining any of the words above, this site may be helpful... Vocabulary Help
1.6
Below there is a document which 4 linear graphs shown and 6 linear equations given. In a paragraph, describe how you matched each equation to its matching graph and the order in which you matched them. What graphical features did you look at or which parts of that equation did you focus on?
Graph A is #8 f(x)= -1/3x-4
Graph B is #2 f(x)= 2x+4
Graph C is #6 f(x)= -1/2x-4
Graph D is #7 f(x)= 1/3x+4
To match the equation with the graph I looked at the graphs y-intercept and I did rise over run and then I would just check the equations to make sure they matched and if they were correct. Also I checked the direction that the graph is going if its positive or negative.
1.7
Below there is a document which 4 linear graphs shown and 12 linear equations given. In a paragraph, describe how you matched each equation to its matching graph and the order in which you matched them. Each graph matches one linear function in slope-intercept form and one linear function in standard form There should be two equations per graph. Did you match equivalent functions first or did you try to match each function to a graph first? What graphical features did you look at or which parts of that equation did you focus on?
Graph A is #4 f(x)= -2x+3 & c 4x+2y=6
Graph B is #1 f(x)= -2/3x+1 & b 2x+3y=3
Graph C is #5 f(x)= 3x+2 & a -3x+y=2
Graph D is #3 f(x)= 2x+3 & d -6x+3y=9
I graphed the y-intercept slope form first and after that I changed all the standard forms to y-intercept slope form and put the matching ones together.
1.8
Using the graph below:
For the first minute Ann drove to school and she went up to a speed of 30 miles per hour. For 4 minutes Ann drove at a steady pace of 30 miles per hour then after those 4 minutes Ann stopped for 1 minute then started driving again going at a steady pace of 40 miles per hour for 3 minutes then her speed went down to a speed of 20 miles per hour for 5 minutes then a minute later she stopped driving.
Answer the following questions:
1.9
In your classroom binder, title a page "Introduction to Graphical Transformations".
f(x)=1/2x
g(x)=1/2(x - 1) + 4
You can use the following document link to help you set up your table of values and graphs if necessary.
After completing the table of values and graphs, in your online journal, describe anything you observe about the relationship of the matching coordinate points. Try to relate this thinking to the equation of g(x).
My table and graph is on this document:
What I noticed about the relationship of these coordinate points is that they are parallel to each other and that they are both linear also that it goes up 4 units and across to the right 1 unit.